UA has a contract lounge in SIN, but I would probably go with a SilverKris lounge (24h/showers/food). I've been to the UA Club in HKG...probably the best UA Club in the world. But I hear TG is even better.
BTW, this guide has information on most of the airports served by *A:
Star Alliance Reference Guide 2014
I usually carry around the PDF version, since it has airport maps (including lounge locations and access policies), and local telephone numbers for most countries, IRROPS policies, etc.
Safe travels.